What happens if the ball is launched at an angle?

Force and Newton’s Laws of Motion
Read more fromChapter Motion and Its Causes

A spectacular demonstration is often used to show the effect of atmospheric pressure. A 55-gallon steel drum is placed on a stand over a propane burner. A quart of water is poured into the drum. The burner will eventually boil the water, filling the drum with steam. When steam has displaced the air, the cap on the drum is tightened and the burner turns off. As the drum cools the steam condenses back to water. The volume of steam is about 1,000 times the volume of water, so when it has condensed it no longer exerts an outward pressure on the drum. But, the atmospheric pressure of 101,000 newtons on each square meter of the drum’s surface is still there. The drum collapses with a thunderous noise.

This demonstration can be done on a much smaller scale with an empty soda can and a bowl of water. Put about ¼” of water in the bottom of the soda can and heat the can on a stove or hot plate. When steam has come out of the hole of the can for several minutes, using a protective glove, quickly turn the can over and put the top into the water. Once again, the steam will condense into water, but because of the small opening, only a small amount of water from the bowl will be able to get into the can. What do you think will happen?

The ball would now have both an initial horizontal velocity and an initial vertical velocity. Again, the horizontal velocity would be constant because there is no force in that direction. Its vertical velocity would be the same as it was when the ball was thrown either down or up. An initial upward velocity is much more interesting, so let’s consider that.

We can specify the initial velocity two ways. First, the way we did before by choosing the horizontal and vertical velocities separately. The second, and more useful way, is to specify the velocity and direction. Suppose a batter hit a baseball at a speed of 90 mph. This speed is 132 ft/s or 40 m/s. The angle could be anything from 90°, a vertical pop-up, down to an angle between 10° and 30° that might be called a line drive to 0° or even a negative angle that would be a ground ball.

The distance the ball travels before hitting the ground depends on both the speed and the angle. If air drag is very small, then the distance is maximum for an angle of 45°. Air drag causes the angle for maximum distance to drop to around 35°. During World War II extensive tables were calculated so that gunners could find the angle for the gun to achieve the desired distance.